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Original Articles

Sub-Independence: An Expository Perspective

Pages 3615-3638 | Received 13 Apr 2011, Accepted 29 Aug 2011, Published online: 05 Sep 2013

References

  • Ahsanullah , M. , Bansal , N. , Hamedani , G. G. ( 1991 ). On characterizations of normal distributions . Calcutta Statist. Assoc. Bull. 41 : 157 – 162 .
  • Ahsanullah , M. , Hamedani , G. G. ( 1988 ). Some characterizations of normal distribution . Calcutta Statist. Assoc. Bull. 37 : 95 – 99 .
  • Bansal , N. , Hamedani , G. G. , Zhang , H. , Behboodian , J. ( 1998 ). A note on Cauchy. chi-square and normal distributions . Technical Report 448 , Marquette University, Dept. of MSCS .
  • Barlow , R. E. , Proschan , F. ( 1981 ). Statistical Theory of Reliability and Life Testing: Probability Models . To Begin With , Silver Spring , MD .
  • Bazargan , H. , Bahai , H. , Aminzadeh-Gohari , A. ( 2007 ). Calculating the return value using a mathematical model of significant wave height . J. Marine Sci. Technol. 12 : 34 – 42 .
  • Behboodian , J. ( 1989 ). Symmetric sum and symmetric product of two independent random variables . J. Theor. Probab. 2 : 267 – 270 .
  • Chung , K. L. ( 1974 ). A Course in Probability Theory . New York : Harcourt, Brace and World .
  • De Paula , A. ( 2008 ). Conditional moments and independence . Amer. Statistician 62 : 219 – 221 .
  • Durairajan , T. M. ( 1979 ). A classroom note on sub-independence . Gujarat Statist. Rev. VI : 17 – 18 .
  • Eaton , M. L. ( 1966 ). Characterization of distributions by the identical distribution of linear forms . J. Appl. Probab 3 : 481 – 494 .
  • Ebrahimi , N. , Hamedani , G. G. , Soofi , E. S. , Volkmer , H. (2010). A class of models for uncorrelated random variables. J. Multivariate Anal. 101:1859–1871.
  • Feller , W. ( 1971 ). An Introduction to Probability Theory and Its Applications . Vol. 2 . New York : Wiley .
  • Hamedani , G. G. ( 1983 ). Some remarks on a paper of Durairajan . Gujarat Statist. Rev. X : 29 – 30 .
  • Hamedani , G. G. ( 1995 ). On symmetric sum of sub-independent random variables . Calcutta Statist. Assoc. Bull. 45 : 119 – 124 .
  • Hamedani , G. G. , Key , E. S. , Volkmer , H. ( 2004 ). Solution to a functional equation and its application to stable and stable-type distributions . Statist. Probab. Lett. 69 : 1 – 9 .
  • Hamedani , G. G. , Tata , M. N. ( 1975 ). On the determination of the bivariate normal distribution from distributions of linear combinations of the variables . Amer. Mathemat. Month. 82 : 913 – 915 .
  • Hamedani , G. G. , Volkmer , H. ( 2003 ). A characterization of symmetric random variables . Commun. Statist. Theor. Meth. 32 : 723 – 728 .
  • Hamedani , G. G. , Volkmer , H. ( 2009a ). Conditional moments, sub-independence and independence . Technical Report 478. Marquette University, Dept. of MSCS .
  • Hamedani , G. G. , Volkmer , H. ( 2009b ). Letter to the Editor . Amer. Statistician 63 : 295 .
  • Hamedani , G. G. , Volkmer , H. , Behboodian , J. ( 2013 ). A note on sub-independent random variables and a class of bivariate mixture . Studia Sci. Math Hungar. 49 : 19 – 25 .
  • Hamedani , G. G. , Walter , G. G. ( 1984a ). A fixed point theorem and its application to the central limit theorem . Arch. Math. 43 : 258 – 264 .
  • Hamedani , G. G. , Walter , G. G. ( 1984b ). On properties of sub-independent random variables . Bull. Iran. Math. Soc. 11 : 45 – 51 .
  • Hamedani , G. G. , Walter , G. G. ( 1985 ). A characterization of reciprocal random variables . Pub. Instit. Stat. Univ. XXX : 45 – 60 .
  • Hamedani , G. G. , Walter , G. G. ( 1987 ). On self-reciprocal random variables . Pub. Instit. Stat. Univ. XXXII : 45 – 66 .
  • Kagan , A. M. , Linnik , Y. , Rao , C. R. ( 1973 ). Characterization Problems in Mathematical Statistics . New York : Wiley .
  • Laha , R. G. , Lukacs , E. ( 1965 ). On a linear form whose distribution is identical with that of a monomial . Pacific J. Math. 15 : 207 – 214 .
  • Lehmann , E. L. ( 1966 ). Some concepts of dependence . Ann. Math. Statist. 37 : 1137 – 1153 .
  • Lukacs , E. ( 1956 ). Characterization of populations by properties of suitable statistics . Proc. Third Berkeley Symp. Mathemat. Statist. Probab. Vol. 2 . Berkeley , CA : University of California Press , pp. 195 – 214 .
  • Lukacs , E. ( 1970 ). Characteristic Functions. , 2nd ed. London : Griffin .
  • Mohammadpour , A. ( 2004 ). Sub-independence and association for Cauchy random variables . XXXVIéme Journées de Statistique , SFDS, http://www.agro-montpellier.fr/sfds/CD/textes.htm .
  • Mohammadpour , A. ( 2010 ). Sub-independence of stable random variables . J. Statist. Theor. Applic. 9 : 29 – 40 .
  • Mohammadpour , A. , Safe , A. ( 2002 ). Sub-independence SαS random vectors with discrete spectral measure . 6th Iran. Statist. Conf. , Tarbiat Modarres University , Tehran , Iran .
  • Trotter , J. F. ( 1959 ). An elementary proof of the central limit theorem . Arch. Math. 10 : 226 – 234 .

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